Predicting mono-jet cross sections in the simplified models
(REF ) and () is complicated
by the fact that the highly energetic initial-state and/or
final-state particles involved in the process are able to
resolve the structure of the top-quark loops that generate the
\({E}_T+ j\)  signal (see the left-hand side of
Figure REF ). Integrating out the top quark and
describing the
interactions by an effective operator of
the form \(\phi G_{\mu \nu }^a G^{a, \mu \nu }\) 
(\(a G_{\mu \nu }^a \tilde{G}^{a, \mu \nu }\) ) with \(G_{\mu \nu }^a\) 
the field strength tensor of QCD and
\(\tilde{G}^{a, \mu \nu } = 1/2 \hspace{0.7113pt}\epsilon ^{\mu \nu \lambda \rho } G^a_{\lambda \rho }\) 
its dual, is in such a situation a poor approximation [1]}, [2]}.
Already in the LHC Run I environment the \(m_t \rightarrow \infty \)  limit
overestimates the exact cross sections by a factor of
5 (40) for \(m_\chi \simeq 10 \,{\rm GeV}\)  (\(m_\chi \simeq 1 \,{\rm TeV}\) ) [3]}.
Removing the top quark as an active degree of freedom becomes
even less justified at \(13 \, (14) \, {\rm TeV}\) , where the
\({E}_T\)  and \(p_{T,j}\)  selection requirements have to
be harsher than at \((7) \, 8 \, {\rm TeV}\)  to differentiate
the DM signal from the SM background. In
order to infer reliable bounds on (REF ) and
(), one therefore has to calculate the
mono-jet cross section keeping the full top-quark mass
dependence. Such
calculations are now publicly available at leading order (LO)
in MCFM [2]} and at LO plus parton shower
(LOPS) in the POWHEG BOX [3]}. Given
that the \({E}_T+ t \bar{t} \, (b \bar{b})\)  signals arise in
the context of (REF ) and
() at tree level (see the right-hand
side of Figure REF ), event generation through
programs like MadGraph5 [6]} is possible,
and UFO model files [7]} from different
groups [8]}, [9]}, [3]} are available for
this purpose.
